Single-ion magnetism in the extended solid-state: insights from X-ray absorption and emission spectroscopy†

Large single-ion magnetic anisotropy is observed in lithium nitride doped with iron. The iron sites are two-coordinate, putting iron doped lithium nitride amongst a growing number of two coordinate transition metal single-ion magnets (SIMs). Uniquely, the relaxation times to magnetisation reversal are over two orders of magnitude longer in iron doped lithium nitride than other 3d-metal SIMs, and comparable with high-performance lanthanide-based SIMs. To understand the origin of these enhanced magnetic properties a detailed characterisation of electronic structure is presented. Access to dopant electronic structure calls for atomic specific techniques, hence a combination of detailed single-crystal X-ray absorption and emission spectroscopies are applied. Together K-edge, L2,3-edge and Kβ X-ray spectroscopies probe local geometry and electronic structure, identifying iron doped lithium nitride to be a prototype, solid-state SIM, clean of stoichiometric vacancies where Fe lattice sites are geometrically equivalent. Extended X-ray absorption fine structure and angular dependent single-crystal X-ray absorption near edge spectroscopy measurements determine FeI dopant ions to be linearly coordinated, occupying a D6h symmetry pocket. The dopant engages in strong 3dπ-bonding, resulting in an exceptionally short Fe–N bond length (1.873(7) Å) and rigorous linearity. It is proposed that this structure protects dopant sites from Renner–Teller vibronic coupling and pseudo Jahn–Teller distortions, enhancing magnetic properties with respect to molecular-based linear complexes. The Fe ligand field is quantified by L2,3-edge XAS from which the energy reduction of 3dz2 due to strong 4s mixing is deduced. Quantification of magnetic anisotropy barriers in low concentration dopant sites is inhibited by many established methods, including far-infrared and neutron scattering. We deduce variable temperature L3-edge XAS can be applied to quantify the J = 7/2 magnetic anisotropy barrier, 34.80 meV (∼280 cm−1), that corresponds with Orbach relaxation via the first excited, MJ = ±5/2 doublet. The results demonstrate that dopant sites within solid-state host lattices could offer a viable alternative to rare-earth bulk magnets and high-performance SIMs, where the host matrix can be tailored to impose high symmetry and control lattice induced relaxation effects.


Introduction
Linearly coordinated transition metal ions can exhibit rstorder spin-orbit coupling which gives rise to large magnetic anisotropy barriers and bi-stability of magnetisation. An example of this is Fe doped in lithium nitride (Li 2 (Li 1Àx Fe x )N). The magnetic anisotropy energy of Li 2 (Li 1Àx Fe x )N exhibits an observed coercivity eld of more than 11 T, exceeding even the largest values observed in rare-earth-based permanent magnets. 1 Consequently, the underlying electronic structure of Li 2 (Li 1Àx Fe x )N is of relevance to the search for alternatives to rare-earth materials. Furthermore, since large single-crystals can be prepared, 2 and the concentration of Fe sites (x) can be controlled, Li 2 (Li 1Àx Fe x )N prepared at low doping concentrations is proposed as single-ion like and therefore a solid-state equivalent 3 to molecular based single ion magnets (SIMs). SIMs are complexes which display slow magnetic relaxation, and magnetic remanence relevant to nano-scale information storage technologies. Notable recent examples of linearly coordinated transition metal SIMs include a Co II (C(SiMe 2 ONaph) 3 ) 2 (where naph is a naphthyl group) complex with a non-auau (d x 2 Ày 2 ,d xy ) 3 (d xz ,d yz ) 3 (d z 2 ) 1 conguration and resultant L ¼ 3 ground-state orbital angular momentum. 4 Another intriguing result are unusual 3d ligand elds. A D Nh crystal eld transforms the 3d-orbitals to a A 1 (3d z 2) singlet at highest energy, followed by a E 1g (3d xz ,3d yz ) doublet at an intermediate energy and a E 2g (3d xy ,3d x 2 Ày 2 ) doublet at lowest energy. However, multi-reference calculations based on the crystal structures of linear complexes, [M I (N(SiMe 3 ) 2 ) 2 ] À (where M ¼ Cr, Mn, Fe, Co) all predict a d-orbital splitting with 3d z 2 at lowest energy. 5 Reasoning for this is due to strong 4s-3d z 2 mixing that weakens the anti-bonding character of the metal ion 3d z 2 orbital. Experimental evidence and the associated implications of 4s-3d z 2 mixing on magnetic properties have been investigated on [Fe I (C(SiMe 3 ) 3 ) 2 ] À . 6 Calculations, based on the crystal structure, propose a a 1g 2 e 2g 3 e 1g 2 ground state conguration with an almost unquenched L ¼ 2 orbital angular momentum. These calculations are supported and found consistent with Mössbauer spectroscopy data 7 and highresolution single-crystal crystallography provides the rst experimental evidence of 3d z 2 2 electron occupation from electron density analysis. 8 However, despite the increasing number of reports of new linear transition metal SIMs 9 there have been very few experimental studies beyond the characterisation of orientation averaged magnetism. In this paper we demonstrate X-ray absorption spectroscopies as an accurate means to characterise the geometric and electronic structure of two coordinate transition metal SIMs. We report results of extended X-ray absorption ne structure (EXAFS), X-ray absorption near edge spectroscopy (XANES), Kb Xray emission spectroscopy (XES) and L 2,3 -edge X-ray absorption spectroscopy (XAS) single-crystal measurements on Li 2 (Li 1Àx Fe x ) N. Each of these techniques have specic sensitivities associated with transition selection rules and generated core-holes. A schematic overview of the spectroscopic techniques and associated transitions are shown in Fig. 1. K-edge XANES probes unoccupied 4p orbitals with 1s / 4p dipole transitions and unoccupied 3d orbitals via the much weaker intensity pre-edge, 1s / 3d, transitions. The technique has particular sensitivity to local coordination symmetry, making it ideally suited for probing distortions from a linear, D Nh , to a bent, C 2v , coordination. Bending leads to a pseudo Jahn-Teller effect that mixes 4p x,y character into 3d xz,yz . This mixing can be clearly identied since it drives strong dipole intensity enhancement in the pre-edge. EXAFS quanties interference effects due to electron scattering from the surrounding atoms. Kb XES involves the ionisation of a 1s electron and the detection of photons emitted from occupied 3p and occupied valence-electrons lling the 1s core-hole. Inter-shell 3d-3p Coulomb exchange makes Kb XES a sensitive probe of 3d spinstate in Li 2 (Li 1Àx Fe x )N as a function of concentration, x. 10 L 2,3edge XAS probes 2p / 3d dipole transitions providing direct experimental access to the ligand eld, related 4s-3d z 2 mixing, spin-orbit coupling and the resultant anisotropy barrier. 11 Magnetisation studies for low Fe doping concentrations show hysteresis is maintained up to 16 K with sweep rates of 15 mT s À1 , 12 which is the largest temperature reported for a transition metal SIM. The effective energy barrier to magnetisation reversal is estimated between 37.1 and 40.2 meV (298.9 and 324.6 cm À1 ). 12 Below a blocking temperature of $10 K relaxation to magnetisation becomes temperature independent, with an exceptionally long magnetic relaxation time of s > 10 4 s. 13 However, despite several theoretical 1,14,15 and experimental 13,[16][17][18][19]55 studies, the electronic structure of Li 2 (Li 1Àx Fe x )N remains a matter of considerable contention. Even the oxidation state of Fe sites has been brought into question by recent ab initio calculations proposing the presence of Li-ion vacancies coupled to Fe II sites. 20 Fig. 2 shows the proposed structure of a single Fe dopant site present within Li 2 (Li 1Àx Fe x )N and possible ground state electronic congurations for both the Fig. 1 Illustration of the Fe X-ray spectroscopic techniques with the associated transitions. (a) L 2,3 -edge absorption probes unoccupied 3d orbitals. Spin-orbit coupling within the 2p 5 core-hole splits the absorption into the 2p 1/2 and 2p 3/2 edges. (b) K-edge pre-edge, edge and EXAFS correspond to 1s absorptions into unoccupied 3d, 4p and continuum respectively. (c) Following the ejection of a 1s electron, Kb XES involves the decay of Fe 3p and occupied valence electrons into the 1s core-hole. Additional open questions arise due to the inaccessibility of low concentration Fe sites embedded within the host structure, and presence or absences of Fe dopant clustering effects and concentration dependencies. In this paper we apply the range of X-ray spectroscopies that selectively characterise different aspects of electronic structure, from which we identify Li 2 (Li 1Àx Fe x )N is a high symmetry solid state SIM clear of stoichiometric vacancies where Fe lattice sites are geometrically equivalent. The geometric and electronic structure of Li 2 (Li 1Àx Fe x )N is compared against molecular based SIMs and important insights into the origin of high temperature magnetic blocking and exceptionally long magnetic relaxation times observed in Li 2 (Li 1Àx Fe x )N are obtained.  Fig. 2. Crystal growth stipulates the crystallographic c axis (magnetic easy-axis) to be oriented surface normal enabling accurate mounting of single crystals to easily perform angular dependence measurements.

K-edge XANES, EXAFS and Kb XES measurements
XANES, EXAFS and Kb XES measurements were performed using the high-resolution uorescence-detection available at the I20-scanning beam-line at Diamond Light Source, UK, and exploiting a four-bounce Si(111) monochromator for spectral purity. 21 The XES measurements were collected by a medipix detector from three Si(531) analyser crystals. XANES and EXAFS measurements were detected with a 64 element Ge detector windowed to the Ka uorescence line. XANES monochromatic energy ranges; 7000-7075 eV, 5 eV step size, 1 s integration (preedge), 7075-7100 eV, decreasing step size 5-0.5 eV, 1 s integration (rising-edge), 7100-7135.5 eV, 0.5 eV step size, 1 s integration (XANES), 7135.5-8100 eV, 0.04Å, increasing integration time from 1-5 s (EXAFS). Kb emission energy ranges; 7025-7080 eV, 0.3 eV step size, 1s int. time (Kb mainline), 7080-7120 eV, 0.2 step size, 5 s integration time (valence-to-core). Several spectra were acquired for each doping concentration. Kb measurements were performed with the incident energy set above the Fe K-edge at 8500 eV. The XANES, EXAFS and Kb measurements were performed at room temperature. Additional Kb measurements at 80 K exhibited negligible difference with respect to measurements at room temperatures. To minimise diffraction induced distortions within EXAFS spectra, crystals of Li 2 (Li 1Àx Fe x )N were ground into powdered pellets where possible. However, it is reported that the host crystal Li 3 N exhibits an additional high pressure phase, of which grinding can induce a partial phase transformation of the Li 3 N lattice from the a to b phase. 22 The XANES spectra of a and b Li 2 (-Li 1Àx Fe x )N differ signicantly. Therefore XANES measurements were performed on both single-crystal and powder samples, from which it was deduced that only the lowest concentration Li 2 (Li 1Àx Fe x )N sample was affected by grinding. For this reason the measurements performed on Li 2 (Li 1Àx Fe x )N for x ¼ 0.0020(5) were on a single crystal while for x ¼ 0.0063(4) and 0.0093 (6) were undertaken on powder samples. Powder samples were formed into pellets and mixed with boron nitride to an appropriate dilution to minimise self-absorption effects. Samples of Li 2 (Li 1Àx Fe x )N were prepared within an argon atmosphere glove-box (<0.5 ppm O 2 and H 2 O) where single crystals and powders were encapsulated with Kapton tape. Measurements were performed within a nitrogen gas atmosphere. XANES and EXAFS analysis was undertaken within the Athena and Artemis packages. 23 Background subtraction was undertaken with a linear tting of the pre-edge and normalisation through a third order polynomial of the post-edge. Bond length (R) and Debye-Waller factor (s) were used as variables of tting for neighbouring lithium and nitrogen atoms. A Levenberg-Marquardt non-linear least-squares minimisation was applied for EXAFS tting. Kb XES spectra are normalised through a trapezoidal integration and the subtraction of a constant. Angular dependent XANES measurements were performed at the BL9-3 beamline at SSRL. The measurements were performed at 10 K in transmission mode on a 1 mm thick single crystal. These measurements were performed with monochromatic energy ranges; 6785-7085 6 eV step size, 1 s integration (pre-edge), 7085-7150 eV, 0.15 eV step size, 1 s integration (rising-edge), 7150-8359.5 eV, 0.5 eV step size, 1 s (post-edge region). Background subtraction of main K-edge XANES isolates the rising-edge peak from which Pearson VII peak tting was undertaken through a least-squares minimisation, Fig. S3. † 2.3 L 2,3 -edge XAS measurements L 2,3 -edge XAS measurements were performed at the I10 high eld magnet end station at Diamond Light Source. Fast energy XAS scans were performed between 690-755 eV with 0.1 eV step sizes. The measurements were performed between 4.5-400 K within an ultra-high vacuum (10 À10 bar). Detection was performed via total uorescence yield in a back-scattering geometry using a 10 Â 10 mm 2 silicon diode with a 150 nm Al cover to lter out electrons. Single crystals of Li 2 (Li 1Àx Fe x )N are too insulating to obtain drain current detected XAS. Single crystals were mounted within an argon glovebox with Torr Seal epoxy resin and transferred to experimental chamber through a nitrogen purged glovebag. Background subtraction of the spectra was performed with a linear tting of the pre-edge (690-700 eV) and normalisation through a linear tting of the post edge (735-750 eV). The 2p 3/2 and 2p 1/2 continuum transitions were subtracted through a double arctangent function 24 (further details see ESI Fig. S4 †).
Ligand eld multiplet simulations of the L 2,3 -edge XAS results were performed using the quantum many-body scripting language, Quanty. 25 The Quanty input les for the simulation of L 2,3 -edge uorescence XAS were adapted from templates generated in Crispy. 26 Multiplet effects are described by the Slater-Condon-Shortley parameters, F k pp , F k pd (Coulomb) and G k pd (exchange), reduced to 80% of the Hartree-Fock calculated values to account for the over-estimation of electron-electron repulsion found for the free ion. The 2p 5 spin-orbit coupling parameter x 2p is found consistent with the atomic value (8.202 eV). The 3d spin-orbit coupling parameters were obtained by tting to the temperature dependence of the L 2,3 -edge XAS, giving x 3d ¼ 0.052 and 0.068 eV for the initial and nal states respectively. The presence of 4s mixing in linear transition metal complexes is known to weaken the 3ds anti-bonding character and reducing the energy of the 3d z 2 orbital. This effect is accounted for in a simple 3d ligand eld model, where the relative energy of the orbitals are adjusted with parameters D q , D t and D s , in the D 6h point group. The ligand eld parameters describe the d-orbital degeneracy and energy splittings of the A 1g (3d z 2) singlet, and two E doublets, E 1g (d xy ,d yz ) and E 2g (d x 2 Ày 2,d xy ). A local linear coordination geometry is characterised by a D Nh ligand-eld, and has equivalence with D 6h when D q ¼ 0. Broadening of the transitions as described by the core-hole lifetime was applied through a Lorentzian function over the L 3 and L 2 edge of 0.35 eV and 0.7 eV full width half maximum (FWHM) respectively. Gaussian broadening due to the instrumental resolution was set to 0.25 eV FWHM and simulated at 4.5 K.

Calculation details
The density functional theory (DFT) calculations presented in this work were performed using the plane-wave pseudopotential DFT method available within the codes Quantum-Espresso 27 and CASTEP. 28 Generalised-gradient approximation for the exchange-correlation energy was selected in the form of PBE functional. 29 Ultraso pseudopotentials were used for PBE and PBE+U calculations, whereas relativistic ultraso pseudopotentials were used for the non-collinear calculations including spin-orbit coupling. The pseudopotentials for use with Quantum-Espresso were taken from the PSlibrary 30 while the pseudopotentials for use with CASTEP were generated self consistently. A kinetic energy cutoff of 90 Ry for the wave function and of 900 Ry for the charge density together with a (6 Â 6 Â 6) Monkhorst-Pack k-point grid were determined as parameters for convergence calculations. A (10 Â 10 Â 10) kpoint grid was instead used for the calculation of the density of states (DOS). Self-consistent calculations were performed to a convergence value of 1 Â 10 À7 eV. Due to the isolated nature of Fe atoms in Li 2 (Li 1Àx Fe x )N, we operated with a 3 Â 3 Â 3 supercell constructed from the hexagonal cell of Li 3 N having space group P6/mmm. The structure was relaxed so that the Fe-N and Fe-Li distances in the rst coordination shells of iron matched the distances evaluated from the analysis of EXAFS results. The reliability of the experimentally evaluated structure for simulations was tested by completing a relaxation up to an energy change of 3 Â 10 À6 eV per atom, which produced a structure yielding a shorter Fe-N distance but a comparable density of states. A smearing of 0.01 Ry was applied to the computed eigenvalues in order to improve the k-point convergence. The angular dependence of Fe K-edge was calculated including the effects of core-hole 31 and using the same k-point grid as previously used for the DOS. Ground state DFT was then expanded by expressing the exchange-correlation potential in terms of local-density band theory via the PBE+U method. 32 The electronic properties were calculated with the simplied, rotational-invariant formulation developed within the linear response approach. 33 An effective U value of 4 eV was included in such calculations, as previously estimated for similar compounds. 34 Angular-momentum dependent orbital occupation was determined with Löwdin charge analysis on top of ground-state, converged DFT wavefunctions. X-ray absorption spectra were computed by extracting the matrix elements for electronic interband transitions from the ground state DFT including the local effects of 1s core-hole as implemented in the code CASTEP. Such calculations were accomplished in the aforementioned supercell, in order to avoid interactions between periodic images of the core excitation. An energy shi of 7110.5 eV was applied to match the experimental data and normalised through trapezoidal integration of simulated spectrum. Transition broadening as a consequence of instrumental resolution (Gaussian) and core-lifetime effects (Lorentzian) was set as 0.2 and 1.25 eV FWHM respectively.

Extended X-ray absorption ne structure (EXAFS)
To precisely quantify the local coordination environment at Fe sites EXAFS measurements were performed on samples with low dopant concentrations, where x ¼ 0.0020(5), 0.0053(4) and 0.0093 (6). The k 3 weighted spectra are presented in Fig. 3a which highlight the EXAFS Fourier transform region as 3 # k # 10Å À1 for x ¼ 0.0020(5) and 3 # k # 12Å À1 for x ¼ 0.0053(4) and 0.0093(6) (E 0 ¼ 7113 eV). Single crystal measurements were performed with E 45 relative to the crystallographic c axis on the lowest concentration (x ¼ 0.0020(5)) sample resulting in signicant Bragg peaks for k values greater than 10Å À1 , requiring a reduced Fourier transform range.
EXAFS tting was undertaken using a model including a single Fe atom dopant within a-Li 3 N as an initial structure (a ¼ 3.652(8)Å and c ¼ 3.870(10)Å, Fig. 2). The selected scattering paths were limited up to a radial distance of 3.5Å; these included two single scattering pathways (Fe-N-Fe, Fe-Li-Fe) and one double scattering path (Fe-N-Li-Fe). Fitting of the experimental data was undertaken for each concentration individually. The EXAFS t parameter results are presented in Table 1. The coordinated nitrogen atoms characterise the rst spectral peak centred at 1.5Å, Fig. 3b, while scattering from the hexagonally bonded lithium atoms in combination with the double scattering path characterise the remaining spectral features. The Fe-N bond lengths were determined to be 1.873 (7) A, 0.062(7)Å shorter than the equivalent Li-N bond length. This nding is consistent with X-ray diffraction results that show caxis contraction and a and b-axis expansion on increasing Fe concentration. 12 39 The EXAFS measurements are consistent with isolated Fe dopants with no indication of clustering evidenced through the lack of strong features beyond the rst structural peak at 1.5Å. While not conclusive there is an observed increase in R-factor with concentration which could be attributed to the requirement of incorporating small contributions from Fe-Fe and Fe-N-Fe scattering paths within the ab plane and along the c axis respectively.
According to combinatorial analysis, the probability of locating n Li ions at the 8 possible neighbouring sites (6 perpendicular and 2 parallel to the crystallographic c axis) for a dopant Fe ion is expressed as: 40 At the highest doped concentration, x ¼ 0.0093 (6), the probability of all 8 neighbouring atoms being lithium is 92.8%, at which point there begins to be a non-negligible requirement of additional scattering pathways to account for Fe dimerisation. However, the number of available independent parameters, dictated by the Nyquist theorem prohibits the inclusion of multiple Fe ions within the model.

X-ray absorption near-edge structure (XANES)
Transition metal oxidation state is frequently characterised by the K-edge threshold energy and the characteristic multiplet effects present within the K pre-edge. 42 Fe K-edge XANES measurements on a polycrystalline sample of Li 2 (Li 1Àx Fe x )N was previously investigated by Niewa et al. 17,43 The threshold energy region of the XANES was found to be dominated by an intense transition centred at 7113 eV. The origin of the 7113 eV peak was assigned by Niewa et al. 17,43 as a K pre-edge (1s / 3d) transition, with enhanced intensity due to 4p-mixing, from which a local C 2v coordination symmetry was proposed. Since bending away from 180 introduces mixing of 4p x character into 3d xz and 4p y into 3d yz due to transformations under the same irreducible representations in C 2v . To further investigate Fe site coordination symmetry, we preformed angular dependent single-crystal Fe K-edge XANES measurements of Li 2 (Li 0.985 -Fe 0.015 )N, Fig. 4 and S2. † The area of the 7113 eV peak for each sample orientation gives the angular dependence of the transition oscillator strength, Fig. 4. Measurements were experimentally limited from 0-45 , where 0 corresponds with Etc and 90 with Ekc. Maximum intensity of the transition is observed at 0 . The variation in intensity as a function of crystal orientation follows a sinusoidal prole with a minimum at 90 ; this is indicative of the two fold symmetry of dipole transitions with 4p x,y orbital character. The XANES of linear Cu I complexes  Table 1. To obtain conclusion of the origin of the 7113 eV peak, and the associated local symmetry of the Fe site, DFT calculations based on a linear geometry were found to accurately reproduce the angular dependent XANES of Li 2 (Li 0.985 Fe 0.015 )N, Fig. 4. Projection of the density of states from this resultant DFT simulation veries the interpreted splitting and degeneracy of the Fe-4p orbitals. Unoccupied character above the Fermi energy (Fig. S5 †) coincides with the expected degeneracy of the 4p x,y orbitals at the energy of the rising edge feature with 4p z orbital character shied to higher energy. In summary, our angular dependent K-edge XANES analysis on Li 2 (Li 0.985 Fe 0.015 ) N identies the local coordination symmetry involves a linear N-Fe-N motif; a conclusion that is further supported by our L 2,3 -edge analysis in the following section. The weak quadrupole allowed 1s / 3d K pre-edge transitions are however unresolved due to overlap with the considerably more intense 7113 eV feature. The absence of a resolvable pre-edge inhibits a ligand eld multiplet analysis to quantitatively assign Fe spin ground-state by K-edge XANES.   valence-to-core peaks at 7098.9 eV and 7110.6 eV (Fig. 5) correspond with metal character present within nitrogen 2s and 2p orbitals respectively. The lack of variation in the relative intensities and energies of these features is consistent with no variation in geometry around the N-Fe-N motif as a function of dopant concentration.

Kb X-ray emission spectroscopy
3.4 L 2,3 -edge X-ray absorption spectroscopy L 2,3 -edge XAS accesses the electronic structure at the 3d orbitals through dipole allowed 2p-3d transitions. Single crystal measurements were performed with Et to the crystallographic c axis and nominal doping concentration, x ¼ 0.015. Fig. 6a shows the Fe L 2,3 -edge total-uorescence spectrum measured at 4.5 K, with L 3 and L 2 edge peaks at 705.7 eV and 720.3 eV respectively. The L 3 -edge exhibits two intense features separated by 1.3 eV whereas the L 2 -edge is dominated by a single intense peak. Both L 2,3 -edges exhibit a series of high energy satellite features indicating the presence of signicant metalligand charge transfer. L 2,3 -edge XAS ligand eld multiplet tting was performed to quantify the 3d electronic structure of dopant sites. Two sets of simulations were performed based on both Fe I and Fe II scenarios. Initial t parameters were extracted from the results of ab initio results reported by Xu et al., 20 see Table S1 and Fig. S6. † Optimisation of the simulated spectral features relative to experiment were obtained through adjustment of the ligand eld parameters (D t and D s ) and include the effect of 4s mixing through the reduction in energy of the 3d z 2 orbital. Agreement with the measured spectrum could only be obtained for the Fe I valence model, with best t parameters of D q ¼ 0, D t ¼ 0.1806 and D s ¼ À0.0257 eV corresponding to an electronic conguration such that d z 2 has the lowest orbital energy, Fig. 6. The simulation quanties the Li 2 (Li 0.985 Fe 0.015 )N dopant site as a Fe I 3d 7 , 4 D 7/2 ion, with a 5 E symmetry ground state resulting from a e 1g 2 e 2g 3 a 1g 2 conguration. The experimentally determined ligand eld splitting is larger than the reported CASSCF result for a [Fe I N 2 Li 14 ] 9+ fragment that gave energies of 0, 0.91, 1.5 eV for a 1g 2 , e 2g 3 and e 1g 2 respectively. 20 The energy reduction in d z 2 is approximately twice the value calculated for the linear monovalent SIM, [Fe(C(SiMe 3 ) 3 ) 2 ] À . 6 Spin-orbit coupling splits the total angular momentum of Fe sites into four Kramers doublets. In order of increasing energy these doublets, M J ¼ AE7/ 2, AE5/2, AE3/2 and AE 1/2, are evenly separated by approximately 2/3x. This splitting characterises the magnetic anisotropy barrier to the slow magnetic relaxation observed in Li 2 (Li 0.985 -Fe 0.015 )N, Fig. 6b. At sufficiently low temperature only the M J ¼ AE7/2 Kramers doublet is populated. The 4.5 K L 2,3 -edge transitions hence emanate exclusively from the M J ¼ AE7/2 doublet. To evaluate the magnetic anisotropy barrier precisely, temperature dependent L 2,3 -XAS measurements were performed. We nd the strong selection rules of L 2,3 -edge XAS makes the technique particularly sensitive to the population of M J states. Therefore, via a series of measurements from 4.5 to 400 K the thermal population of M J excited states can be experimentally deduced from changes in the line shape of the L 3 -edge spectrum. The temperature dependence is most clearly identied through the relative peak intensity for Peak 1 (P 1 ), E ¼ 706.1 eV versus Peak 2 (P 2 ), E ¼ 707.3 eV at the L 3 -edge, Fig. 7. Modelling the temperature dependent ratio of P 1 and P 2 through Maxwell-Boltzmann statistics the thermal population of the excited states can be achieved through the equation:  where E i represents the energy of the four M J AE7/2, AE5/2, AE3/2 and AE1/2 states (each evenly separated by 2/3x), k B is the Boltzmann constant and A and c are multiplicative and scaling factors. The inlay of Fig. 7 shows L 3 -edge peak ratio (P 1 /P 2 ) versus inverse absolute temperature (1/T) for Li 2 (Li 1Àx Fe x )N. Fitting to eqn (1) gives x ¼ 52.2 AE 4.97 meV (421 AE 40.08 cm À1 ), signicantly greater than the atomic value for Fe I of 44.8 meV. 6 Typically, the free ion spin-orbit coupling parameter represents the upper limit for spin-orbit coupling, where bonding leads to only decrease x. However, atomic spin-orbit coupling is strongly dependent on electron conguration, particularly on the number of 3d electrons. 46 For instance, the 3d atomic spin-orbit coupling for a 3d 6 4s 1 conguration is x 3d ¼ 51 meV, approximately 6 meV greater than the value for a 3d 7 conguration. 47 Therefore, we propose that the measured value of x is greater than the 3d 7 atomic value due to strong 4s-3d z 2 mixing. Previously reported measurements of magnetic relaxation for Li 2 (-Li 1Àx Fe x )N at low doping concentrations gave the effective energy barrier to magnetisation reversal (U eff ) between 37.1 and 40.2 meV (298.9 and 324.6 cm À1 ). 12,19 This is close to 34.80 AE 3.31 meV (280.7 cm À1 ) the energy splitting between the ground M J ¼ AE7/2 and rst excited AE5/2 doublet determined from our variable temperature L 2,3 -edge XAS analysis. To our knowledge the application of variable temperature L 3 -edge XAS has not been previously reported. Therefore, we performed supporting calculations into the origin of this effect. This enabled us to conrm the same temperature dependence in the simulated spectra and test the validity of our tting method (Fig. S7 †). Furthermore, to identify the origin of the temperature dependence Fig. S8 † shows the calculated L 2,3 -edge XAS spectra associated with each thermally populated Kramer's doublet of the ground-state J ¼ 7/2 manifold. The calculations identify the individual intensity contributions to P 1 and P 2 for each M J doublet.
Since rst-order spin-orbit coupling in Li 2 (Li 1Àx Fe x )N is a manifestation of an odd electron count within the E 2g orbitals, the relationship between non-linearity due to N-Fe-N bending and the magnetic anisotropy barrier can be explored through the introduction of a D q crystal eld parameter. Fig. 8 shows the effect of including a non-zero D q energy on the simulated Fe L 3edge. To maintain the measured anisotropy energy of Li 2 (-Li 0.985 Fe 0.015 )N, the magnitude of D q must be less than 1 meV. This result supports our angular dependent K-edge XANES analysis, demonstrating the strict N-Fe-N linearity imposed within the a-Li 3 N matrix.

Conclusion and outlook
We have characterised the local geometric and electronic structure of Fe dopant sites in Li 2 (Li 1Àx Fe x )N via K-edge XANES and EXAFS, L 2,3 -edge XAS and Kb XES as a function of x, with particular attention to low values of x, where Fe sites are sufficiently isolated and hence perform as single ion magnets. The complementary use of element specic X-ray spectroscopy techniques unambiguously answers a multitude of questions that had limited quantitative understanding of this system. Kb XES analysis rules out previous arguments 20 for a divalent subspecies in Li 2 (Li 1Àx Fe x )N at low x concentration. EXAFS analysis shows no evidence of preferential Fe clustering at low dopant concentrations. L 2,3 -edge XAS measurements in conjunction with ligand eld multiplet simulations conclude Fe sites are monovalent with a 4 D 7/2 ground state of 4 E symmetry resultant from a a 1g 2 e 2g 3 e 1g 2 conguration. The energetic order of the 3d orbitals is affected by strong 4s-3d z 2 mixing that results in a fully occupied 3d z 2 at lowest energy. The strong inuence of 4s-3d z 2 mixing in reducing the destabilisation of 3ds antibonding has long been reasoned by DFT and more recently by quantum chemistry calculations. 6,48 It is shown that L 2,3 -edge XAS enables experimental quantication of 3d z 2 energy reduction. The large 3d z 2 energy reduction contributes to raising the anisotropy barrier in Li 2 (Li 1Àx   comparison with other linear SIMs where s is within a range of seconds and less. To further understand the origin of the unusually long Li 2 (Li 1Àx Fe x )N relaxation time, we have analysed the geometric structure and coordination symmetry around Fe dopant sites. EXAFS analysis nd both Fe-N bond lengths as 1.873(7)Å, which is exceptionally short for two-coordinate Fe I . The shortness of the Fe-N bonds suggests strong Fe-N p bonding, facilitated by the D 6h point symmetry providing equal N 2p pmixing into both 3d xz and 3d yz orbitals. 50 Further evidence of this is observed via strong satellite intensities present in the L 2,3 -edge XAS spectra. The N-Fe-N angle is analysed by K-edge XANES through single-crystal angular dependence of an intense, low energy, 7113 eV peak. A ligand eld interpretation is backed up by DFT calculations, assigning the transition as being associated with unoccupied 4p x,y orbitals, from which it is deduced that the N-Fe-N bonding does not deviate from linear. This conclusion is supported by ligand eld multiplet simulations that indicate that D q induced degeneracy breaking of 3d xy and 3d x 2 Ày 2 cannot exceed 1 meV for the measured energy reversal barrier to be maintained.
Together the X-ray spectroscopy results identify Li 2 (Li 1Àx Fe x ) N as an ideal model system clean of stoichiometric vacancies where Fe sites are geometrically equivalent. The doping of Fe ions into the lithium nitride host matrix enables control of inter-SIM distances, from which dipolar elds can be minimised. The introduction of Fe sites displace Li ions at 2c positions causing a local bond contraction of 0.062(7)Å with respect to the equivalent Li-N bond. The linear N-Fe-N core is supported through 3d xz,yz -Np mixing and indirectly by the hexagonal lithium nitride lattice, that acts to drive bond shortening and rigorous linearity, in a similar but more direct way than dispersion force stabilisation observed in other linear molecular complexes, including Fe[N(SiMe 3 )Dipp] 2 . 38 Previous theoretical studies have identied the crucial inuence of reduced symmetry and Renner-Teller vibronic coupling on the magnetic relaxation time in two coordinate Fe SIMs. 51 It is proposed that the combination of a short Fe-N bond, related strong 3dp bonding, and high point symmetry imposed by the hexagonal lithium nitride lattice contribute to suppress vibronic effects, resulting in increased magnetic relaxation times with respect to other linear SIMs. The high point symmetry of the solid-state host lattice exhibit less disorder with respect to large inorganic coordination complexes. The high symmetry of the crystal host lattice and geometric equivalence of Fe dopant sites, result in a very low propensity for dislocation-induced strain type variations in local symmetry and easy axis directions, consistent with the extreme eld dependence reported in Li 2 (Li 1Àx Fe x )N. 13,19 The quantication of electronic structure reported here provides insights relevant for the advance of high performance magnets free from rare-earth metals. The extraordinary electronic and magnetic properties of Li 2 (Li 1Àx Fe x )N, highlights the potential of doping paramagnetic ions within high symmetry solid-state lattices. Another area of potential relevance is nanoscale information storage for which there is currently considerable effort devoted to depositing coordination complexes with SIM properties on surfaces. 52,53 An even distribution of SIM dopant sites within a high symmetry host lattice crystal or thin lm 54 offers an interesting alternative method, with additional degrees of freedom for controlling local symmetry and lattice phonon dispersion.

Conflicts of interest
There are no conicts to declare.